Problem: Solve for $x$. Enter the solutions from least to greatest. $2x^2 - 24x + 54 = 0$ $\text{lesser }x = $
$\begin{aligned} 2x^2 - 24x + 54&= 0 \\\\ 2(x^2-12x+27)&=0 \end{aligned}$ Now let's factor the expression in the parentheses. $x^2-12x+27$ can be factored as $(x-3)(x-9)$. $\begin{aligned} 2(x-3)(x-9)&=0 \\\\ x-3=0&\text{ or }x-9=0 \\\\ x=3&\text{ or }x=9 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= 3 \\\\ \text{greater }x &= 9 \end{aligned}$